Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
نویسندگان
چکیده
Recommended by Mohamed Khamsi Let S be a left amenable semigroup, let S {T s : s ∈ S} be a representation of S as Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition, let {μn} be a strongly left regular sequence of means defined on an S-stable subspace of l∞ S , let f be a contraction on C, and let {αn}, {βn}, and {γn} be sequences in 0, 1 such that αn βn γn 1, for all n. Let xn 1 αnf xn βnxn γnT μn xn, for all n ≥ 1. Then, under suitable hypotheses on the constants, we show that {xn} converges strongly to some z in F S , the set of common fixed points of S, which is the unique solution of the variational inequality 〈 f − I z, J y − z 〉 ≤ 0, for all y ∈ F S .
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